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Ratio Calculator 3 Numbers

Ratio Simplification Formula:

\[ a : b : c = \frac{a}{g} : \frac{b}{g} : \frac{c}{g} \]

Where \( g \) is the GCD of a, b, and c

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1. What is a Three-Number Ratio Calculator?

Definition: This calculator simplifies a ratio of three numbers to its smallest whole number equivalent by dividing each term by their greatest common divisor (GCD).

Purpose: It helps simplify complex ratios for easier interpretation and comparison in mathematics, chemistry, cooking, and other fields.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ a : b : c = \frac{a}{g} : \frac{b}{g} : \frac{c}{g} \]

Where:

Explanation: The calculator finds the largest number that divides all three input numbers exactly, then divides each term by this GCD.

3. Importance of Ratio Simplification

Details: Simplified ratios are easier to understand, compare, and use in calculations while maintaining the same proportional relationship.

4. Using the Calculator

Tips: Enter any three positive numbers. The calculator will return the simplified ratio and the GCD used for simplification.

5. Frequently Asked Questions (FAQ)

Q1: What if my numbers have decimals?
A: The calculator handles decimal inputs, but for best results, multiply all numbers by 10, 100, etc. to make them integers before simplifying.

Q2: What if two numbers are the same?
A: The calculator will still work correctly, and the simplified ratio will reflect the relationship between all three numbers.

Q3: Can I use this for more than three numbers?
A: This calculator is designed for three numbers, but the same principle applies to ratios with more terms.

Q4: What if my numbers have different units?
A: Ratios require all terms to have the same units. Convert all numbers to the same unit before calculating.

Q5: What does a GCD of 1 mean?
A: A GCD of 1 means the numbers are co-prime (no common divisors other than 1), and the ratio is already in simplest form.

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